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provided by Elsevier - Publisher Connector HISTORIA MATHEMATICA 3 (1976), 185-202

LOUIS CHARLESKARPINSKI, HISTORIAN OF MATHEMATICSAND CARTOGRAPHY

BY PHILLIP S, JONES, THE

Summary

Louis C. Karpinski was best known for his publica- tions on the history of mathematics, and secondarily as a historian of cartography. This survey of his life includes an account of his contributions to the teaching of mathematics and of his avocational interests as a collector, chess player, and gadfly attacking what he saw as poor thinking and abuses of power in both the univer- sities and in the public domain. It is followed by a note on archives, a list of the Ph.D. theses he supervised, and a complete bibliography.

1. EARLY LIFE AND EDUCATION Louis C. Karpinski was born August Sth, 1878 in Rochester , and died in Winter Haven, Florida on January ZSth, 1956. Both of his parents had come to this country asimmi- grants. Henry H. Karpinski had come from Warsaw, Poland via England at the age of 19. Louis' mother, Mary Louise Engesser, had emigrated from Gebweiler in Alsace. Henry Karpinski left his position with the Eastman Company in Rochester to take his family to Oswego, New York where he set up a cleaning and dye- ing business which was later continued by his older son, Henry. In 1894, Louis Karpinski graduated from high school in Oswego in the English and German curriculum. He received a Teacher's Diploma from Oswego State Normal School in 1897, and he began his teaching career, at the age of nineteen, in the schools of Southold, Long Island. In January 1898, he went to teach in the normal department of Berea College in Kentucky. In 1899, Karpinski entered where he played championship chess, having earlier won a state champion- ship in 1896, and won honors in public speaking. The title of the oration for which he won a gold medal in the Cornell University Woodford Prize Contest of 1901 was "The Southern Mountaineer". This reflects his experience in Berea as well as a life-long concern for people and social-economic problems. In this same year he also earned both money and experience teaching in the private Cascadilla School in Ithaca. Louis Karpinski completed his A.B. at Cornell in 1901 and in the same year enrolled in the American College of the Kaiser 186 P. S. Jones HM 3

Wilhelms-Llniversitzt zu Strassburg. In 1903, he was awarded the degree Dr. Phil. Nat. after submitting a number theoretic thesis (1) (parenthetical numbers refer to the appended bibliography, bracketed numbers to the notes) to a committee chaired by Heinrich Weber and including Theodore Reye and F. Braun. 2. WORK AND DEVELOPING INTERESTS His occupations for the next few years reflect Karpinski’s continuing interest in teaching and his somewhat tense, vigorous activity. In 1903-1904, he wasincharge of physics and chemis- try at Oswego State Normal College and of arithmetic in its practice school. Summers, he taught at New York University (1904) and the Chatauqua Institution at Chatauqua, New York (1905-1907). In 1904, he had accepted a position as instructor in mathematics at the University of Michigan, and in 1905 he married Grace Woods. He had met her at Cornell University where she had enrolled on a scholarship in 1899. The daughter of a county school superintendent in Lockport, New York, she taught physics, chemistry, Greek and Latin at a school in New Jersey for a year after graduating from Cornell in 1904. The Karpinskis had six children, Robert Whitcomb, Mary, Loui se, Ruth, Joseph Louis and Charles Elwin. They were active in community affairs and belonged to the Congregational church. Louis taught a publicly advertised bible class, “Studies in the Acts and Epistles” as one of the McMillan Hall Association Study courses, and served as the piano accompanist for choral groups on the strength of the year of lessons which he had received at the age of sixteen. He also gave a lecture on the history of arithmetic as a part of the University’s summer program of lectures and entertainment. In 1906, 1907, and 1908 he returned to New York State to lecture in the teachers’ institutes which were commonly sched- uled at the beginning of school each fall. 3. DEVELOPMENTAS A HISTORIAN In spite of the fact that at various times Louis had anemia, diabetes, and heart trouble, he was always active pro- fessionally as well as in church, community, and political affairs. In the University he progressed to a full professor- ship in 1919, and to professor emeritus upon his retirement in 1948. However, his professional career was strongly redirected by the year which he spent (1909-1910) as a Teachers College Fellow and Extension Lecturer at Teachers College, . He had been encouraged in historical interests by his department chairman, W. W. Beman, who himself had written historical papers as well as secondary school texts. Interest in the history of mathematics at the University of Michigan was further heightened by the presence of Alexander Ziwet (81)) Chairman of the Department of Mathematics of the College of HM3 187

Engineering. Ziwet, who also was trained abroad, had a wide interest in mathematical literature, a large and fine personal library, which he eventually gave to the University (64), and had also published historical articles. However, the most direct influence on Karpinski was that of with whom he worked at Teachers College. Although they were later rivals in a friendly sense, at least so far as Karpinski was concerned, their joint publication The Hindu Arabic Numerals (12) was Karpinski’s first book and is still one of the basic references on this subject. 4. KARPINSKI AS A BIBLIOGRAPHER The rivalry with David Eugene Smith and Columbia University, at least in the mind of Karpinski, developed after he returned to the University of Michigan and began to build there a collec- tion of source materials in the history of mathematics. He did this by badgering librarians and alumni for funds as he scanned book catalogues and traveled to visit dealers and auctions. In later years he would say,“1 always said Michigan had the better collection - even when it didn’t”. This statement was made especially with respect to Columbia’s collection which later became the Smith-Plimpton Collection, when two bibliophiles gave their private collections to Columbia University. However, he was also aware of the collection at Brown University built up through the efforts of R. C. Archibald. It is hard to know which was his more basic urge, that of the collector, or that of the competitor. In either case, he competed as a collector to the advantage of the University of Michigan and of the history of mathematics and cartography. Professor Karpinski’s scholarly contributions as a bibli- ographer were a natural concomitant of his collecting urge. His Bibliography of Mathematical works Printed in America through 1850 (110) with the several supplements published in Scripta Mathematics (111, 113, 118) is commonly cited merely as “Karpinski” by dealers in Americana, and has been a basic refer- ence for studies of the early history of mathematics in America. He also published bibliographies of early algebraic (112) and trigonometric (114) works. This interest appears also in his cartographic work, where his Bibliography of the Printed Maps of Michigan, 1804-1880 (130) is still authoritative. Bibliographies are, of course, essential to scholarly work, particularly to historical work. They become tools for future scholars and are themselves a scholarly product, not merely appendages to papers. Karpinski’s influence and indirect products are also to be observed in the theses of his students [1], some of which inc- luded bibliographies as essential parts of the body of their research. Items 69, 71, 73, 74, 101 and 116 of the list of his publications show his interest in early American arithmetic. Items 121, 126, 128 are bibliographies relating to cartography, 188 P. S. Jones HM 3 and 158 deals with early military publications. This latter was done in collaboration with Colonel Thomas M. Spaulding, who also gave the University of Michigan many rare mathematical works. 5. RESEARCH IN THE HISTORY OF MATHEMATICS Returning to Louis Karpinski's major interest in the history of mathematics, we find his initial work with the Hindu Arabic numerals being extended to include early European algor- isms (13, 21, 22, 31, 59, 79, 82, 83, 89, 100, 103) and algebraic manuscripts (14, 15, 20, 23, 24, 32, 41, 83). The often-cited book Robert of Chester's Latin Translation of the Algebra of Al-Khowarizmi (41) was the culmination of his work in the latter area. It also typifies his interest in orig- inal sources and manuscripts, which was served by trips to European libraries and depositories. A survey of his publications on algorisms also suggests the fruitfulness of his contacts with historians and scholars in other fields. These were sometimes represented by joint pub- lications and sometimes by acknowledgements, prefaces, or addenda in articles listed under other names. In addition to David Eugene Smith and Thomas Spaulding we can list Karpinski's son-in-law, Charles N. Staubach (loo), and E. G. R. Waters (79), a romance language specialist at Oxford, with both of whom he worked on algorisms, and his colleagues Martin Luther D'Ooge and Frank Egleston Robbins of the Greek Department with whom he shared in the production of a translation and commentary on Nichomachus of Gerasa's Introduction to Arithmetic (75). Arthur S. Aiton (159) was a colleague in the History Department; Adelaide M. Fiedler (68) was a student. Harry Y. Benedict and John W. Calhoun (53) were colleagues at other schools, and Charles Bathe (149) was a descendant of Benjamin Franklin. In discussing the difficulties of translating mediaeval Latin manu- scripts Professor Karpinski mentioned, orally, that his wife's background in this language had been an aid in his work on the Robert of Chester manuscript (15, 41). 6. THE IHISTORY OF CARTOGRAPHY The challenge of collecting, love for scholarship and source materials, and his large family, motivated several other Karpinski activities and publications. He conceived the project of photographing source materials for American history, espec- ially manuscript maps in libraries and archives in France, Spain and Portugal. During a sabbatical year, 1926-27, he photo- graphed over 650 maps, many from the sixteenth and seventeenth century. In the process he was able to secure assistance in overcoming bureaucratic and military red-tape and opposition from the Duke of Alba, in Spain, and Paul Painleve', a French mathematician who was then Minister of War and later became Premier. These difficulties and the rumour that such photo- graphic privileges might be denied to others in the future made HM3 Louis Charles Karpinski 189

his collection of photographs even more valuable. It was pur- chased in whole or part by a number of American libraries. The collection in the William L. Clements Library of American History at the University of Michigan contains 773 photographs occupying fourteen large volumes. However, Professor Karpinski’s most scholarly and author- itative cartographical work is represented by the two volumes commissioned by the Historical Commission of the State of Michigan, and published by them in 1931, Bibliography of the Printed Maps of Michigan 1804-1880 (130) and Historical Atlas of the Great Lakes and Michigan to Accompany the Bibliography of the Printed Maps of Michigan (131). A number of additional cartographic papers are noted in the bibliography. 7. ENTREPRENEURAND COLLECTOR Louis Karpinski’s entrepreneurial tendencies were suggested in the previous section where we noted his combining of a ser- vice to scholarship and history with a commercial program, selling photographs of maps to libraries. The proceeds from these sales, the sale of his own collection of maps and atlases, and the income from occasional articles for magazines and news- papers supplemented the income of a college professor who not only liked to travel himself, but who also wished to take his large family abroad. Between 1921 and 1928, he published nearly sixty articles in the Dearborn Independent (148), a weekly news- paper owned by Henry Ford and edited by W. J. Cameron,who became a friend and traveling companion to the Karpinskis. In the early 1930’s, he sold the Karpinski Collection of maps to Yale University for a substantial sum to be paid over a period of years. The collection, which is estimated to have contained nearly a thousand items, is currently being combined with Yale’s von Wieser Collection of Maps and Atlases to form the basis of the Thorne CollectionofCartography and Geography in Yale University’s Beinecke Library. After his retirement, Professor Karpinski continued to combine business with pleasure. He bought atlases and books in varied fields from dealers and at auctions, loaded them in his car, and called at many libraries to help them improve their holdings and to introduce famous rarities into collections at small colleges. As a text writer, he produced three books, an integrated text for a freshman course (53)) a table of logarithms (52), and his History of Arithmetic (73). The first book was an excellent example of a type of text which never “caught on”. The book was an integrated treatment of college algebra, func- tions, including trigonometric functions, and analytic geometry. It stressed the idea of a function, graphs, and applications. In the opinion of this writer it is still in many ways ahead of its time! It did appear in a second edition and in a Russian 190 P. S. Jones HM3

translation. It is interesting to note that the History of Arithmetic has recently been reprinted after many years of being out of print. 8. OTHER SERVICES TO THE HISTORY OF MATHEMATICS Professor Karpinski served the history of mathematics and science in a variety of roles in addition to that of researcher and bibliographer. In particular, he was an expositor and trans mitter of new historical developments to those with less time, expertise, or contact with the field. This was done via radio talks, speeches at teachers’ conventions, expository articles and reviews. He was, for example, the invited speaker at the first organizational meeting of the Mathematical Association of America at Cleveland, Ohio, in December 1915. The records of that meeting show that he gave an illustrated lecture on “The Story of Algebra”. The records do not show the nature of the illustrations but one can conjecture that he used either an opaque projector or slides. His interest in photography and slides dates back at least to his time at Columbia University, because his correspondence with David Eugene Smith shows that he borrowed slides to show in Michigan after his return from New York. In 1931, he was the designer of the four series of slides depicting the history of arithmetic, algebra, geometry, and higher mathematics which were automatically projected on the four sides of a central column of the area devoted to mathe- matics in the Hall of Science at the Century of Progress Expos- ition (world’s fair) in Chicago, in 1932. The appended bibliography of Karpinski’s publications includes his reviews because often they were extended, including corrections, additional data, and sources so as to be scholarly expositions in their own right. The critical side of his nature and his continuing concern for the pedagogy of mathematics showed up most often in his reviews of texts and of books intended for teacher education. He was sharply critical of “educators” when he felt they were superficial in their thinking or scholarship (78, 150, 151), but he gave substantial praise to others (35, 58, 77). One review of a book on the teaching of mathematics concluded with “where it was new it was not right, and where it was right it was not new”! (51) He regularly taught professionalized subject matter courses in algebra and geometry for secondary school teachers as well as courses in the history of arithmetic and algebra, geometry and trigonometry, and the history of the calculus. His doctoral students and their theses titles are listed in note [l]. He served as an associate editor of Scripta Mathematics from its founding in 1932 until his death, and was active in a variety of organizations. We noted earlier his presence at the organizational meeting of the Mathematical Association of America . He was its Librarian 1921-22, and in 1924 he gave a paper, “Early American Arithmetics”, at the first meeting of the Michigan Section [2]. HM3 Louis Charles Karpinski 191

9. MEMBERSHIPS, OFFICES, HONORS In addition to the usual memberships of a professional mathematician and historian (American Mathematical Society, Mathematical Association of America, Deutsche Mathematiker Vereinigung) he belonged to such pedagogically oriented organiz- ations as the National Education Association, Central Assoc- iation of Science and Mathematics Teachers, Michigan School- masters Club, and the Michigan Academy of Science, Arts, and Letters. He was active in the History of Science Society, being a member of its council in 1926-28, 1934, 1940, vice-president in 1936-39, and president in 1943. In the American Association for the Advancement of Science he was a vice-president and chairman of Section L, the Historical and Philological Sciences in 1923-24 and 1938-39. He was a member of Sigma Xi and Membre Effectif #14 of the Comitc’ Internationale d’Histoire des Sciences. In 1932, he was one of the members of the Michigan George Washington Bicenten- nial Commission, and in 1937 President Franklin D. Roosevelt appointed him, G. D. Birkhoff, and Arnold Dresden as the delegation to the Descartes Tercentenary in Paris. His talk at that event was later printed in Science (107).

10. MISCELLANEOUS INTERESTS AND ACTIVITIES As has been suggested earlier, Louis Karpinski was a bit of a gadfly, an activist somewhat ahead of his time. In faculty meetings and committees he proposed faculty representation on the Board of Regents and attacked the private practices and fees of professors in the medical school. He toured southern coll- eges speaking for the newly developed T.I.A.A. (Teachers Insur- ance and Annuity Association) program. In later years he attacked the rates and rate setting procedures of public util- ities in hearings and in the press. He listed himself in the 1948 Who's Who as an expert on utility rates as well as a mathe- matician and historian of science. In 1947 when Beardsley Rum1 was to address the prestigious Detroit Economic Club on his proposed subsidies to older citi- zens, Karpinski personally distributed to the audience pamphlets which he had written analyzing and opposing the “Rum1 Plan”. His stands and attacks were not always moderate and in at least one instance led to hard feelings. Professor Karpinski attended the meeting of the American Council of Learned Societies as president of the History of Science Society. At these sessions he strongly objected to a report on modern language teaching, and proposed a resolution that professional persons called upon to give expert testimony or advice to Congress or other govern- ment agencies should be required to make a declaration of all their commercial connections with groups interested in the sub- ject on which they were to give testimony or advice (161). Other officers of the History of Science Society felt that 192 P. S. Jones HM 3

Karpinski had given the impression that the views he had expressed were those of the Society. After some bitter corres- pondence, Karpinski resigned as president. As another evidence of the modernity of some of his out- looks, one can note that he introduced a resolution favoring the metric system into the 1920 joint meeting of the American Mathematics Society, the Mathematical Association of America, and the American Association for the Advancement of Science. Perhaps the best ending for this section is the self- description in his annual faculty report for 1938: "Democrat, reformed Republican".

11. CONCLUSION It is impossible to estimate the ultimate effect of Louis Karpinski's life and work. It has been spread by the enthusiasm and teaching of the many young people who passed through his classes and by the scholars who read his work and were motivated and directed by it. Some undergraduates had to grow in maturity to appreciate the prodding of his impatience with those who, for lack of effort or insight, could not reply to a question, and to recognize the excitement and uniqueness of exposure to his broad historical information and insight. In later years they returned and wrote to express their thanks for facts and interests which had grown in utility and pleasure over the years. Editors and proofreaders found that the mass of materials which he collected from wide-ranging searches broughtwith it much work for them. However, hundreds of students recalled him, his courses, and his counseling with enthusiasm for many years. Later generations of historians are still benefitting from his work.

ARCHIVAL NOTES There are pictures, a number of boxes of letter, reprints, and information about Professor Karpinski in the Bentley Library of the Michigan Historical Collections at the University of Michigan. A picture of him as vice-president of the A.A.A.S. is in The Scientific Monthly, vol. 50, p.90.

ACKNOWLEDGEMENTS It is a source of regret that Mary Karpinski Casey's death came only a few days before she could have read the final draft of this story. Her assistance with anecdotes, family materials, and comments on an earlier draftwereenthusiastic and helpful. Facts and impressions were also given by Professor WarnerG. Rice, who is a former Director of the University of Michigan Library and who was a neighbor of the Karpinskis, by Professor Howard H. Peckham, Director of the William L. Clements Library, HM3 Louis Charles Karpinski 193

and by the Curator of Maps, Alexander Vietor, and the staff of the Yale University Library.

NOTES 1. Louis C. Karpinski's doctoral students and their disser- tations, in chronological order, were: Susan Rose Benedict, A Comparative Study of the Early Treatises Introducing into Europe the Hindu Art of Reckoning, 1914. Concord, N.H.: The Rumford Press, 1916. vi + 126 pp. Irby Coghill Nichols, A Comparative Study of Fractions of the Early Treatises on the Hindu Art of Reckoning, 1916. John David Bond, The Development of Trigonometric Methods Down to the Close of the XVth Century, 1920. This dealt largely with Richard Wallingford's Quadripartitum and was printed in Isis in parts as follows: 3 (1921), 215-323; 4 (1921-22), 313- 314; 5 (1922-23), 99-115, 339-363. Franklin Wesley Kokomoor, The Teaching of Elementary Geometry in the Seventeenth Century, 1926. Isis 10 (1928), 21-32, 367-415; 11 (1928),85-110. Sister Mary Leontius Schulte, Additions in Arithmetic, 1483-1700, to the Sources of Cajori's “History of Mathematical Notations" and Tropfke's "Geschichte der Elemantar-Mathematik", 1934. Ann Arbor, Michigan: Edwards Brothers, Inc., 1935. x + 99 pp. Sister Mary Thomas B Kempis Kloyda, Linear and Quadratic Equations, 1550-1660, 1935. Ann Arbor, Michigan: Edwards Brothers, Inc., 1938. xii + 141 pp. Sister Mary Claudia Zeller, The Development of Trigonometry from Regiomontanus to Pitiscus, 1944. Ann Arbor, Michigan: Edwards Brothers Inc., 1946. vi + 119 pp. Phillip Sanford Jones, The Development of the Mathematical Theory of Perspective and its Connections with Projective and Descriptive Geometry with Especial Emphasis on the Contributions of Brook Taylor, 1947. 2. Carl B. Boyer, "The First Twenty-Five Years", The Mathe- matical Association of America: Its First Fifty Years, 1972. Published by the M.A.A.; edited by Kenneth 0. May. See also the six index entries under Karpinski in this publication.

BIBLIOGRAPHY OF LOUIS C. KARPINSKI NOTE: All publications are arranged chronologically in each of three categories: mathematics, cartography, and miscellaneous.

MATHEMATICS 1. ijber die Verteilungen Der Quadratischen Reste. Inaugural Dissertation der Mathematischen und Naturwissenschaftlichen Facult'Eit der Kaiser Wilhelms - Universitgt zu Strassburg. 194 P. S. Jones HM 3

Strassburg (1903) and Journal f. die reine u. angew. Math. 127(1905), l-19 2. Non Euclidean Geometry Proc. of the Michigan Schoolmasters' Club (1905), 83-87 3. The Decimal System of Numbers Pop. Sci. Mon. 74(1909), 490-498 4. Reform in the Teaching of Mathematics The School Review 17 (1909), 267-271 5. The Program of the International Commission Science 29(1909), 605-606 6. Preliminary Report of the International Commission on Secondary Mathematics (a translation), School Sci. and Math. 9(1909), 103-113 7. Finger Reckoning American Education 12(1908-1909), 449-450 8. A Unique Collection of Arithmetics Pop. Sci. Mon. 75(1910), 226-235. A review of Smith's Rara Arithmetica. 9. Review of A History of the Logarithmic Slide Rule and Allied Instruments, in Science 32(1910), 666-668 lO.Jordanus Nemorarius and John of Halifax Amer. Math. Mon. 17(1910), 108-113 11. Number Amer. Math. Mon. 18(1911), 97-102 12. The Hindu-Arabic Numberals (with David Eugene Smith) 1911 Boston (Ginn and Company) vi + 160 pp. 13.Hindu Numberals in the Fihrist Bib. Math. (3)11(1911), 121-124 14. An Italian Algebra of the Fifteenth Century ibid., 209-219 15. Robert of Chester's Translation of the Algebra of Al Khowarizmi ibid., 125-131 16. The Hindu-Arabic Numerals Science 35 (1912), 969-970 17.Mathematics Chapter VI in Charles Hughes Johnson High School Education 1912 New York (Scribner's), 128-145 18. Augrim Stones Modern Language Notes 27(1912), 206-209 19.The History of Mathematics in the Recent Edition of the Encyclopaedia Britannica Science 35(1912), 29-31 20. The Algebra of Abu Kamil Shoja, ben Aslam Bib. Math. (3)12(1912), 40-55 21. Hindu Numerals Among the Arabs Bib. Math. (3)13(1913), 97-98 22. The "Quadripartitum Numerorum" of John of Meurs ibid., 99-114 23.The Algebra of Robert Recorde, The Whetstone of Witte ibid., 223-228 24.John Caswell ibid., 248-249 25. Notes on the Word "Algebra" Modern Language Notes 28(1913), 93 26. Simplified Arithmetic The American Boy (NOV. 1913) 27. Review of Isis Amer. Math. Mon. 20(1913), 131-132 28. Review of H. E. Hawkes, Higher Algebra ibid., 194-195 29. Review of E. H. Barker, Computing Tables and Mathematical Formulas Arranged for the Use of High Schools and Colleges ibid., 282 HM3 Louis Charles Karpinski 195

30. Review of C. I. Palmer, Practical Mathematics in Michigan ~lurnnus 19(1912-1913), 478-479 31.The Algorism of John Killingsworth English Historical Review 29(1914), 707-717 32.The Algebra of Abu Kamil Amer. Math. Mon. 21(1914), 37-48 33.Efficiency in the Schoolroom Journal of Ed. 80(1914), 489 34. Practical Arithmetic ibid., 603-605 35. Review of D. E. Smith and Mikami, A History of Japanese Mathematics in Science 40(1914), 675-676 36. Review of Mikami, The Development of Mathematics in China and Japan in Science 40(1914), 676-677 37. Review of D. E. Smith, The Teaching of Arithmetic and A. W. Stamper, The Teaching of Arithmetic in Amer. Math. Mon. 21(1914), 85-86 38. Review of W. B. Ford and Charles Ammerman, Plane and Solid Geometry in Michigan Alumnus 2O(Feb. 1914), 283 39. Arithmetic for the Lumberman Amer. Lumberman (April 25, 1914), 52-53 40. How to Compute Interest American Boy (Mar. 1914) 41. Robert of Chester's Latin Translation of the Algebra of Al-Khowarizmi, with an Introduction, Critical Notes and an English Version. University of Michigan Studies, Humanistic Series, volume XI, and New York (Macmillan) 1915 vii + 164~. 4 plates 42.A Rule to Square Numbers Mentally School Sci. and Math. 15(1915), 20-21 43.The History of Algebra Proc. of the Fifteenth Ann. Meet. Cent. Assoc. of Sci. and Math. Teachers (1915), 232-234 44. Review of , A Budget of Paradoxes in Science 42(1915), 729-731 45. Review of C. I. Palmer and C. W. Leigh, Plane Trigonometry with Tables in Michigan Alumnus 21(1914-1915), 214-215 46. Review of J. C. Brown and L. D. Coffman, How to Teach Arith- metic in School and Society 2(1915), 893-894 47.Arithmetic for the Farm The Educator Journal 16(1915), 132- 135 48. The Teachingof ElementaryMathematics School andsociety 5( 1917), 78 49. The Decimal Point Science 45(1917), 663-665 50. Algebraical Developments Among the Egyptians and Babylonians Amer. Math. Mon. 24(1917), 257-265 51. Review of P. Klapper, The Teaching of Arithmetic in School and Society 8(1918), 441-442 52. Four Place Logarithmic and Trigonometric Tables Together with Interest Tables 1918 Ann Arbor (George Wahr) 30 PP. 53. Unified Mathematics (with Harry. Y. Benedict and John W. Calhoun) 1918 and 1922 Boston (D.C. Heath) viii + 522~. A Russian translation was published in Moscow in 1926 54. Answers toKarpinski's UnifiedMathematics 1919 Boston (Heath) 21 p 55. Origins et Developpement de 1'Algebre Scientia 26(1919), 89-101 Reprinted in English in School Sci. and Math. 23(1923), 54-64 196 P. S. Jones HM3

56. New Activities in the HistoryofScience Science 50(1919), 213-214 57. The Parallel Development of Mathematical Ideas, Numerically and Geometrically School Sci. and Math. 20(1920), 821-828 58. Review of D. E. Smith, The Sumario Compendioso of Brother Juan Dies, the Earliest Mathematical Work of the New World in School and Society 14(1921), 83-84 59. Two Twelfth Century Algorisms Isis 3(1921), 396-413 60. Hermann von Helmholtz Scientific Mon. 13(1921), 24-32 61.A Brief Historical Consideration of the Metric System Science 53(1921), 156-157 62. Gli Scienziati Italiani Science 53(1921), 237-238 63. Review of Julius Ruska, Zur Altesten Arabischen Algebra und Rechenkunst in Isis 4(1921), 67-70 64.The Ziwet Collection Amer. Math. Mon. 28(1921), 484 65. Michigan Mathematical Papyrus, No. 621 Isis 5(1922), 20-25 1 plate 66.The Methods and Aims of Mathematical Science School Sci. and Math. 22(1922), 718-723 67.An Egyptian Mathematical Papyrus in Moscow Science 57(1923), 528-529 68. The Terminology of Elementary Geometry (with Adelaide M. Fiedler) School Sci. and Math. 24(1924), 162-167 69. The First Arithmetic in the United States School and Society 19(1924), 349-350 70.Two Unpublished Monuments to American Scholarship Science 59(1924), 502-503 71. Colonial American Arithmetics Bibliographical Essays: a Tribute to Wilberforce Eames 1925 Cambridge (Harvard Univ. Press) 243-248 1 plate 72. Apropos of Egyptian Mathematics Amer. Math. Mon. 32(1925), 41 73. The History of Arithmetic 1925 Chicago (Rand McNally) xxi + 200 pp. Reprint 1965 New York (Russell and Russell) 74. The Earliest Known American Arithmetic Science 63(1926), 193-195 75. Nichomachus of Gerasa, Introduction to Arithmetic Translated by Martin Luther D'Ooge with studies in Greek arithmetic by Frank Egleston Robbins and Louis Charles Karpinski. Univer- sity of Michigan Studies, Humanistic Series, vol. XVI 1926 New York (Macmillan) 1936 Ann Arbor (Univ. of Michigan Press) Third printing 1946. x + 318 pp. 76.New Light on Babylonian Mathematics Amer. Math. Mon. 33(1926), 325-326 77. Three Notable Books on the History of Mathematics of the Greeks Science 67 (1928), 241. Review of books by Paul ver Eecke on Archimedes, Apollonius, and Diophantos. 78.Review of D. E. Smith and W. D. Reeve, The Teaching of Junior High School Mathematics in School and Society 27(1928), 300- 302 HM3 Louis Charles Karpinski 197

79. Introduction to A Thirteenth Century Algorism in French Verse by E. G. R. Waters Isis 11(1928), 45-47 8O.The Unity of the Hindu Contributions to Mathematical Science Scientia 43( 1928), 381-388 81. Alexander Ziwet - in Hemoriam (with J. W. Bradshaw, T. H. Hildebrandt and Peter Field) Bull. Amer. Math. Sot. 35 (1929), 259-260 82.An Early Printed Italian Arithmetical Treatise Arch. di Storia della Scienza (Archeion) 11(1929), 331-335 83.The Italian Arithmetic and Algebra of Master Jacob of Florence, 1307 ibid., 170-177, + 2 facsimiles 84.Mathematics and the Progress of Science School Sci. and Math. 29(1929), 126-132 85.The Permanent Nature of the Necessity for Mathematics in the Secondary Schools The Math. Teacher 22(1929), 197-202 86.Michigan Papyrus 620, the Introduction of Algebraic Equations in Greece (with F. E. Robbins) Science 70(1929), 311-314 87.Recent Progress in the History of Ancient Mathematics ibid., 622-624 88.Mathematical Shortcuts for Engineers and Architects 1929 Detroit (The Multi-Color Company) (pawhlet) 89.Early Algorisms in French Atti de1 Cong. Int. dei Mat., Bologna, 3-10 Settembre 1928 6(1931), 455-458 90. Rare Mathematical Books in the University of Michigan Library Scripta Math. 1(1932), 63-65 91. Numbers through the Ages and Around the World 1933 Chicago (Colortext Publications) 12 PP. 92. Linear and Quadratic; Straight and Square School Sci. and Math. 33(1933), 34-39 93. The Unity of Algebra and Geometry ibid., 515-516 94. The Historical Development of Fractions Contemporary Guide in the Teaching of Arithmetic, ed. Raleigh Schorling, J. R. Overman, Walter 0. Shriner 1933 Ann Arbor (Edwards Brothers) pp. 76-78 95. Historical Evolution of the Idea of the Unknown Quantity ibid., 107-109 96. Les Liaisons entre les Contributions de la Mathematique Grecque Ancienne et le Progres de la Science et de la Civilisation Deltion 1(1934), 20-26 97.Mathematics and the Progress of Science (in Turkish and English, translated by Salin Murat Bey) Muhendis Mektebi Mecmuasi (Journal of the College of Engineering, University of Turkey) 1934, 767-776 98. Mathematics of the Orient ibid., 777-786. Also in School Sci. and Math. 34(1934), 467-472 99. The Importance of Greek AlgebraicalProblems Isis 22(1934), 104-10s 100. Introduction to An Anglo-Norman Algorism of the Fourteenth Century by Charles N. Staubach ibid., 23(1935), 121-124 198 P. S. Jones HM3 lOl.The Elusive George Fisher "Accomptant" - Writer or Editor of Three Popular Arithmetics Scripta Math. 3(1935), 337-339 102. An Exhibition of Early Textbooks on College Mathematics from the Collection in the University Library 1935 Ann Arbor 4 PP. Pamphlet prepared for the meetings (Sept. 9-13 1935) of the Math. Assoc. of Amer., Amer. Inst. of Statisticians, and Amer. Math. Sot. 103.The First Printed Arithmetic of Spain Osiris 1(1936), 411- 420 104. New Light on Babylonian Mathematics Amer. J. of Semitic Lang. and Lit. 52(1936), 73-80 105. Simultaneous Quadratics Solvable in Quadratic Irrationalities Amer. Math. Mon. 43(1936), 362-366 106. Is there Progress in Mathematical Discovery and Did the Greeks Have Analytical Geometry? Isis 27(1927), 46-52 107. Descartes and the Modern World Science 89(1939), 150-152 108. The Origin of the Mathematics as Taught to Freshmen Scripta Math. 6(1939), 133-140 109.A Problem of Presentation in Trigonometry Nat. Math. Maq. 13(1939), 240-241 110. Bibliography of Mathematical Works Printed in America through 1850 1940 Ann Arbor (University of Michigan Press) xxvi + 697 pp. (Note that items 111, 113, 118 below are supplements to this.) 111. Supplement to the Bibliography of Mathematical Works Printed in America through 1850 Scripta Math. 8(1941), 233-236 112.Algebraical Works to 1700 Scripta Math. 10(1944), 149-169 113. Second Supplement to the Bibliography of Mathematical Works Printed in America through 1850 Scripta Math. 11(1945), 173-177 114.The Place of Trigonometry in the Development of Mathematical Ideas ibid., 268-272 115. Bibliographical Check List of All Works on Trigonometry Published up to 1700 A.D. Scripta Math. 12(1946), 267-283 116. Mathematics in Latin America Scripta Math. 13(1947), 59-63 117.A Notable Contribution to the Bibliography of the Mathe- matical Sciences Scripta Math. 14(1948), 73-74. Essentially a review of Karl KBfer, Ein Beitraq zur Geschichte und Theorie des Kaufmsnnischen Rechnens. 118. Third Supplement to the Bibliography of Mathematical Works Printed in America through 1850 Scripta Math. 20(1954), 197-202

CARTOGRAPHY (See also Miscellaneous Works, especially in the Dearborn Independent) 119. Review of Joachim Bensaade, Histoire de la Science Nautique Portuqaise a 1'Epoque des Grandes Descouvertes, Collection de Documents Publies par Ordre du Minister-e de 1'Instruction HM 3 Louis Charles Karpinski 199

Publique in Hispanic American Historical Review 5(1922), 718- 721 120. Review of Edward Luther Stevenson, Terrestrial and Celestial Globes, their History and Construction Including a Consider- ation of their Value as Aids in the Study of Geography and Astronomy in Science 56(1922), 199-201 121.Atlases of the Sixteenth and Seventeenth Century William L. Clements Lib. Bull. 4(1924) 4 pp. 122.American Uses of Globes before 1800 Science 61(1924), 243- 244 123.Early Maps of the Mississippi Valley Arranged for the Meeting of the Mississippi Valley Historical Association Held in the Library, May 1, 1925 William L. elements Lib. Bull. 7(1925) 124.Artistic Maps of Early Years The Print Connoisseur 6(April 1926) 23 pp. + pl. 125.They Thought California Was An Island ibid., 7(July 1927), 119-160 126. Manuscript Maps Relating to American History in French, Spanish, and Portuguese Archives Amer. Hist. Rev. 33( 1928), 328-330 127.The First Printed Map of America New York Herald Tribune Books (August 18, 1929), 23 128. Edited: Early Maps of Carolina and Adjoining Regions, Together with Early Prints of Charleston from the Collection of Henry P. Kendall; Catalogue Compiled by Priscilla Smith 1930 Boston 47 pp. Second edition 1937 Charleston 67 pp. 4 pl. 129.The First Map with the Name America Geog. Rev. 20(1930), 664-668 130. Bibliography of the Printed Maps of Michigan, 1804-1880 (Including discussions of Michigan maps and map-makers by William Lee Jenks) 1931 Lansing (Michigan Hist. Commiss.) 539 pp. + 36 pl. 131.Historical Atlas of the Great Lakes and Michigan 1931 ibid. iv + 104 pp. 132. Cartographical Collections in America Imago Mundi 1(1935), 62-64 133.Early Maps of Carolina 1937 Charleston 11 pp. Address given at Gebbes Art Gallery 134.Maps and Notes taken from "Bibliography of the Printed Maps of Michigan" Michigan Hist. Mag. (Winter 1943) 135.Michigan and Great Lakes upon the Map, 1636-1802 Michigan Hist. Mag. 29(1945), 291-312 136. Early Michigan Maps, Three Outstanding Peculiarities ibid., 506-511 137.Maps of the Explorers from the Collection of Dr. Louis C. Karpinski Michigan Conservation 34(1965), 30-33. Taken from his Bibliography of the Printed Maps of Michigan 200 P. S. Jones HM3

MISCELLANEOUS 138.Visions The Independent 1909 139. Slate New Encyclopedia of Education 1913 New York (Macmillan) 140. Michigan Graduates in Mohammedan Countries Michigan Alumnus 19(1912-1913), 127-131 141. Standards in Education School Sci. and Math. 14(1914), 745 142. Review of Roger Bacon, Essays in Science 40(1914), 894-895 143.Michigan in the Orient The Missionary Review of the World 27(1915), 747-754 144. Reviews of eight books on the history of science, including Barnard, The Casting Counter and the Counting Board and Cajori, William Ouqhtred: The History of Science School and Society 8(1918), 741-749, and, in Italian, Boll. Bib. e Storia delle Sci. Mat. 21(1919), 15-27 145.Hindu Achievement in Exact Science, a Study in the History of Scientific Development Amer. Math. Mon. 26(1919), 298-300. Contrasts views in B. K. Sarkar, Astronomical Observatories of Jai Sinqh with those in G. R. Kaye, Archeological Survey of India. 146. Professorial Budgets Michigan Alumnus (1919). Reprinted in School and Society 10(1919), 678-680 147.Astronomical and Mathematical Rarities in the University of Michigan Library Michigan Alumnus 25(1919), 592-597 148. The Dearborn Independent (a weekly magazine published by Henry Ford. The courtesy of the Ford Archives in making their file of back issues available is gratefully acknow- ledged. The following articles varied from one to three pages in length.) New Light on Christopher Columbus 24 May 1924, 14. The Evolution of the Map of the World 31 May 1924, 4. How the Great Lakes Were Placed on the Map 19 July 1924. A Psalter Now Worth $75,000 16 August 1924, 3. An Inter- national Congress of Mathematicians 27 Sept 1924, 15. Almanacs of our Forefathers 18 Ott 1924, 12. The Almighty Dollar - A Brief History 15 Nov 1924, 5. How News First Got into the Newspapers 22 Nov 1924, 3. Returning to the Old Route from Europe to America 29 Nov 1924, 14. Royal Books and their Rich Bindings 3 Jan 1925, 4. Preserving the Written Record 10 Jan 1925, 9. American Libraries Lead in Service 21Feb1925,9. plapping out America 7 Mar 1925, 13. The Story of Eliot's Bible 11 April 1925, 12. Mapping the Mississippi Valley 2 May 1925, 12. In Ye Days of Ye Horne-Boke 9 May 1925, 12. How We Got Our Present Calendar 30 May 1925, 8. Early American Bibles 13 June 1925, 28. How France Aided American Liberty (with Charles Bathe) 4 July 1925, 4. A Rare Book Now - New England Primer of Pre-Independence Days 18 July 1925, 24. Mapping the Great Northwest 1 Aug 1925, 21. Mapping the Northwest Passage 8 Aug 1925, 24. Mapping Alaska Took Centuries 15 Aug 1925, 20. Putting Muscle Schools on the Map 24 Ott 1925, 28. HM3 Louis Charles Karpinski 201

Why and How it became 'America' 14 Nov 1925, 14. The Men of the Mayflower as Fathers of the Republic 12 Dee 1925, 29. They Thought California was an Island 30 Jan 1926, 24. Early Arithmetics Published in America 13 Feb 1926, 20. Ye Knife-- Ye Fork--Ye Spoon 2 Ott 1926, 8. The First Advertisement in English 30 Ott 1926, 24. Who Discovered America? 25 Dee 1926, 21. Who Wrote Mother Goose? 8 Jan 1927, 25. Belgium Tries to Get on Her Feet 15 Jan 1927, 1. The Can Opener in France 29 Jan 1927, 22. The Opening of the Civil War 12 Feb 1927, 8. The Game and Playe of the Chesse 30 Apr 1927, 14. American Life of 200 Years Ago 21 May 1927, 20. The Manipulation of the Pseta 28 May 1927, 3. Lights and Shadows of Spain 4 June 1927, 5. The First Scientific Map of the World 11 June 1927, 3. The Gypsy Cave Dwellers of Spain 2 July 1927, 20. When New York Goes to Paris 9 July 1927, 9. English Hunting as Seen in the Advertisements 9 July 1927, 14. Fascinating Walled City of Feudal Times 9 July 1927, 16. Books for Cooks 23 July 1927, 24. Low Wages in France 10 Sept 1927, 3. France and America--an Industrial Contrast 24 Sept 1927, 1. Early American Speller 8 Ott 1927, 9. Early American Schools 15 Ott 1927, 9. Discovers Apocryphal Gospel 22 Ott 1927, 23. Villegaigon and Antarctic France 12 Nov 1927, 4. Beaumarchais, Friend of America Part 1 19 Nov 1927, 4; part 2 26 Nov 1927, 12. The Magazines of Colonial Days 3 Dee 1927, 8. Early English and American Road Books 10 Dee 1927, 12. An Interesting Letter by Benjamin Franklin 10 Dee 1927, 28. Spain Under the Dictator 17 Dee 1927, 4. (The author listed in the Dearborn Independent was "Our European Correspondent." flowever, the files of the Ford Archives show him to have been Karpinski). Concerning the French Academy 12 Dee 1927, 24. Broadsides (Poster Printing) 24 Dee 1927, 20. 149. How France Aided American Liberty Our Debt to France with Charles Bathe 1926 New York (Washington Lafayette Institu- tion), 41-51. (See similar article in 148, 4 July 1925.) 150. The Textbook Racket University of Michigan Radio Speeches 1933 University of Michigan Official Publication No. 44, 25-29. 151. The Presentation of Scientific Facts to Children in School and Society 38(1933), 247-248. Review of Achieve- ments of Civilization Number 2. 152. Sam Loyd Dictionary of American Biography 11(1933), 479-480. 153. George H. Mackenzie ibid. 12(1933), 92-95. 154. Nicolas Pike ibid. 597-598. 155. Paul C. Morphy ibid. 13(1934), 193-194. 156. Harry N. Pillsbury ibid. 14(1934), 606. 157. The Obligations of a University Teacher Who Writes Popular Science School and Society 48 (1938), 338-340. 158. Early Military Books in the University of Michigan Libraries with Thomas M. Spaulding. 1941. Ann Arbor (Univ. of Michigan Press), xvi+371 pp. 37 pl. 202 P. s. Jones HM 3

159. Chronology of Events of Scientific Importance in North and South America in the Sixteenth Century Archeion 22(1940), 382-397 with Arthur S. Aiton. (Archive de Historia de la Scienca (NS)l, 2 Feb 1941). 160. The Progress of the Copernician Theory Scripta Math. 9(1943), 139-154. 161. National Learned Society Groups and the Public Interest Science 97(1943), 422-423. 162. Review of George E. Nunn The Geographical Conceptions of Columbus in Mississippi Valley Historical Review (Dee 1925)) 422-3 163. Arithmetic Centenarians, Textbooks with a Long Life Scripta Math. 2(1933-1934), 34-40 164. Review of Johannes Tropfke Geschichte der Elementar-Mathematik in Systematischer Darstellung mit Besenderer Beriichsichtigung der Fachwijrter in ibid. 351-3 165. Nicholas Pike (1743-1819) Diet. Am. Biog. XIV 1934 New York (Scribner’s) 166. Copernicus, Representative of Polish Science and Learning Natnl. Math. Mag. 19(1945), 343-348. Also published in Polish in Polonia Almanac 1945 Detroit

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CSHPMLSCHPM The Canadian Society for History and Philosophy of Mathe- matics/Soci&& canadienne d’histoire et de philosophie des mathe- matiques will meet at Universite Lava1 (Quebec City) on 4 June 1976. An invited address will be presented by Prof. Asger Aaboe (Yale) entitled “The scientific foundations of ancient and medie- val cosmology, ” followed by several sessions of contributed papers. There will also be an annual meeting and election of officers.

A directory of members of the Society is being prepared and will be distributed in the near future. There will be an increase in the subscription rate for HM to members from $6 to $8, begin- ning in 1977 (volume 4). There will be no increase in dues ($4). Persons interested in joining the Society should contact the Secretary, Charles V. Jones, Department of Computer Science and Mathematics, Atkinson College, York University, Downsview, Ontario, M3J 2R7.